# Fair Division of Multi-layered Cakes

arXiv: https://arxiv.org/abs/2208.00726 · HTML: https://mlsanity.com/paper/2208.00726/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 29 references that are in the map.
- First posted on arXiv 1 Aug 2022.

## Builds on (most cited first, 5 of 5)

- [A Discrete and Bounded Envy-Free Cake Cutting Protocol for Any Number of Agents](https://mlsanity.com/paper/1604.03655/) (2016)
- [A Discrete and Bounded Envy-free Cake Cutting Protocol for Four Agents](https://mlsanity.com/paper/1508.05143/) (2015)
- [Fair Division of Time: Multi-layered Cake Cutting](https://mlsanity.com/paper/2004.13397/) (2020)
- [Envy-free division of multi-layered cakes](https://mlsanity.com/paper/2106.02262/) (2021)
- [The Query Complexity of Cake Cutting](https://mlsanity.com/paper/1705.02946/) (2017)

## Abstract (arXiv)

We consider multi-layered cake cutting in order to fairly allocate numerous divisible resources (layers of cake) among a group of agents under two constraints: contiguity and feasibility. We first introduce a new computational model in a multi-layered cake named ``a pair of knives''. Then, we show the existence of an exact multi-allocation for two agents and two layers using the new computational model. We demonstrate the computation procedure of a feasible and contiguous proportional multi-allocation over a three-layered cake for more than three agents. Finally, we develop a technique for computing proportional allocations for any number n≥ 2a3 of agents and 2a3 layers, where a is any positive integer.